Stochastic modelling and assessment of long-span precast prestressed concrete elements failing in shear

The shear behaviour of reinforced and prestressed concrete structures has been extensively studied over the last decades. However, there are still numerous open questions, concerning, e.g. the effects of normal-shear force interaction and material properties on shear performance. While the elastic behaviour of structures can be accurately captured by existing analytical approximations available within code standards, the description of the plastic behaviour of prestressed concrete elements occurring before typically quasi-brittle shear failure requires nonlinear analysis. Therefore, most prestressed concrete structures are designed to utilise only the elastic capacity of the material to avoid the performance of a complex nonlinear finite element analysis (hereinafter NLFEA) of pre-failure behaviour. In the case of mass-produced precast elements, however, the higher cost of performing NLFEA to provide valuable information on the complete loading of such element's history might be justified and economically beneficial. NLFEA can give much more objective information on a structure's performance and ultimate capacity, its cracking behaviour and failure indicators which can be utilised for the optimisation of the design, maintenance and inspection of produced structural elements. However, deterministic NLFEA cannot capture the naturally uncertain character of structural response. Current code standards provide a framework for NLFEA using several safety formats. The fully probabilistic approach remains the most general, straightforward and least conservative way of considering uncertainties, however. The stochastic modelling of a precast element's shear response requires the performance of a series of fracture-mechanical experiments with material samples, the evaluation of stochastic features of material parameters, and the use of identified random parameters as inputs for highly accurate nonlinear finite element models of destructive experiments. The information on material uncertainty is then used for the virtual statistical simulation of Monte Carlo type to obtain the probability distribution of structural resistance. This paper aims to describe the application of stochastic NLFEA to the shear behaviour simulation of a for wide-span prestressed reinforced concrete lightweight roof element. Extensive experimental studies on small specimens and scaled and full-scale girders have been performed to acquire the required information for the implementation of complex material laws in advanced probabilistic nonlinear numerical analyses. This information is used together with advanced monitoring systems to investigate stochastic features of shear structural response, the probabilistic safety level in terms of code-based design levels, and the experimental findings.